Distance and Displacement
Understand Distance and Displacement for GCSE Physics with this free worksheet and full mark scheme — Foundation and Higher exam-style questions with worked answers for AQA, Edexcel and OCR. Distance is a scalar measuring how far an object moves, while displacement is a vector including the direction from start to finish.
Free downloads
These worksheets and mark schemes are original, written for Virtus Academy and checked against the current AQA, Edexcel and OCR specifications. Every worksheet comes with a full mark scheme.
Topic overview
Distance is how far an object moves, and it is a scalar quantity with no direction. Displacement includes both the distance from the start point and the direction of that straight line, so it is a vector.
Walking around a circular track and returning to the start covers a distance equal to the circumference, but the displacement is zero, because the finish point is the same as the start.
This distinction matters because vectors can cancel. Distance always accumulates as you travel, but displacement can increase, decrease or return to zero depending on the direction of travel. Both are measured in metres.
Revision notes
The definitions
Distance is how far an object moves. It is a scalar, so it has no direction.
Displacement measures the distance and direction in a straight line from the start point to the finish point. It is a vector.
When they differ
If an object travels in a straight line without turning back, distance and displacement have the same magnitude.
If the object changes direction or returns towards the start, they differ. A complete circuit gives a distance equal to the perimeter but a displacement of zero.
Typical values
Useful reference values: a person walks at about 1.5 m/s, runs at about 3 m/s, and cycles at about 6 m/s.
The speed of sound in air is about 330 m/s. These are worth knowing for estimation questions.
Key points
- Distance is a scalar with no direction.
- Displacement is a vector with direction.
- Both are measured in metres.
- A complete circuit gives zero displacement.
- Distance always accumulates.
- Displacement can decrease or return to zero.
Worked examples
Example 1
State the difference between distance and displacement. [2 marks]
Model answer
Distance is how far an object has moved and is a scalar with no direction (1 mark). Displacement is the straight-line distance and direction from the start point to the finish point, and is a vector (1 mark).
Example 2
A runner completes one lap of a 400 m track. State the distance travelled and the displacement. [2 marks]
Model answer
The distance travelled is 400 m (1 mark). The displacement is zero, because the runner finishes at the same point as they started (1 mark).
Example 3
Explain why displacement can be smaller than distance travelled. [2 marks]
Model answer
Displacement is measured in a straight line from start to finish (1 mark), so any change of direction during the journey means the straight-line distance is less than the total path length (1 mark).
Common mistakes
Saying displacement is always equal to distance.
They are equal only for straight-line motion without turning back.
Omitting direction from displacement.
Displacement is a vector, so the direction must be given.
Saying displacement cannot be zero.
It is zero whenever the object returns to its starting point.
Using different units for the two.
Both are measured in metres.
Exam tips
- Always state the direction when giving a displacement.
- Check whether the object returns towards the start.
- Use the circuit example to explain zero displacement.
- Learn the typical speed values for estimation questions.
Key terms
- Distance
- How far an object moves, a scalar quantity.
- Displacement
- Straight-line distance and direction from start to finish.
- Scalar
- A quantity with magnitude only.
- Vector
- A quantity with magnitude and direction.
Related topics
Written and reviewed against the current AQA, Edexcel and OCR specifications. Spotted an error? Let us know.